證明?$：(1) ∵ AF$?是?$⊙O$?的切線，
?$∴ AF⊥OA， $?
?$∴ ∠OAF=90°.$?
?$∵ CE$?是?$⊙O$?的直徑，
?$∴ ∠CBE=90°， $?
?$∴ ∠OAF=∠CBE.$?
?$∵ AF//BC，$?
?$∴ ∠BAF=∠ABC， $?
?$∴ ∠OAF-∠BAF=∠CBE-∠ABC，$?
即?$∠OAB=∠ABE， $?
?$∴ AO//BE$?
?$(2) ∵ \widehat{EA}=\widehat{EA}， $?
?$∴ ∠ABE=∠ACE. $?
?$∵ OA=OC，$?
?$∴ ∠ACE=∠OAC， $?
?$∴ ∠ABE=∠OAC.$?
由?$(1)$?知，?$∠OAB=∠ABE， $?
?$∴ ∠OAB=∠OAC， $?
?$∴ AO$?平分?$∠BAC$?
